Balanced subgroups of totally projective groups
\textit{F. Richman} and \textit{E. Walker} showed that balanced subgroups of totally projective groups are not necessarily totally projective [J. Algebra 56, 145-167 (1979; Zbl 0401.20049)]. Nevertheless, the author proves the following remarkable theorem: Let B and B' be balanced subgroups of reduced totally projective p-groups A and A', respectively. If B and B' have the same Ulm-Kaplansky invariants and if A/\(B\cong A'/B'\), then B and B' are isomorphic. Moreover, there is an isomorphism from A onto A' which maps B onto B'.
scientific article; zbMATH DE number 3867590